# bipartite_projection

From igraph v1.0.0
by Gabor Csardi

##### Project a bipartite graph

A bipartite graph is projected into two one-mode networks

- Keywords
- graphs

##### Usage

```
bipartite_projection(graph, types = NULL, multiplicity = TRUE,
probe1 = NULL, which = c("both", "true", "false"), remove.type = TRUE)
```

##### Arguments

- graph
- The input graph. It can be directed, but edge directions are ignored during the computation.
- types
- An optional vertex type vector to use instead of the
vertex attribute. You must supply this argument if the graph has no`type`

vertex attribute.`type`

- multiplicity
- If
`TRUE`

, then igraph keeps the multiplicity of the edges as an edge attribute. E.g. if there is an A-C-B and also an A-D-B triple in the bipartite graph (but no more X, such that A-X-B is also in the graph), then the multiplicity of the A-B e - probe1
- This argument can be used to specify the order of the projections in the resulting list. If given, then it is considered as a vertex id (or a symbolic vertex name); the projection containing this vertex will be the first one in the result list. This argu
- which
- A character scalar to specify which projection(s) to calculate. The default is to calculate both.
- remove.type
- Logical scalar, whether to remove the
`type`

vertex attribute from the projections. This makes sense because these graphs are not bipartite any more. However if you want to combine them with each other (or other bipartite graphs), then it is wo

##### Details

Bipartite graphs have a `type`

vertex attribute in igraph, this is
boolean and `FALSE`

for the vertices of the first kind and `TRUE`

for vertices of the second kind.

`bipartite_projection_size`

calculates the number of vertices and edges
in the two projections of the bipartite graphs, without calculating the
projections themselves. This is useful to check how much memory the
projections would need if you have a large bipartite graph.

`bipartite_projection`

calculates the actual projections. You can use
the `probe1`

argument to specify the order of the projections in the
result. By default vertex type `FALSE`

is the first and `TRUE`

is
the second.

`bipartite_projection`

keeps vertex attributes.

##### Value

- A list of two undirected graphs. See details above.

##### Examples

```
## Projection of a full bipartite graph is a full graph
g <- make_full_bipartite_graph(10,5)
proj <- bipartite_projection(g)
graph.isomorphic(proj[[1]], make_full_graph(10))
graph.isomorphic(proj[[2]], make_full_graph(5))
## The projection keeps the vertex attributes
M <- matrix(0, nr=5, nc=3)
rownames(M) <- c("Alice", "Bob", "Cecil", "Dan", "Ethel")
colnames(M) <- c("Party", "Skiing", "Badminton")
M[] <- sample(0:1, length(M), replace=TRUE)
M
g2 <- graph_from_incidence_matrix(M)
g2$name <- "Event network"
proj2 <- bipartite_projection(g2)
print(proj2[[1]], g=TRUE, e=TRUE)
print(proj2[[2]], g=TRUE, e=TRUE)
```

*Documentation reproduced from package igraph, version 1.0.0, License: GPL (>= 2)*

### Community examples

Looks like there are no examples yet.